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Acta Physica Sinica

TEMPORAL ASPECTS OF ABSORPTIVE TWO-PHOTON OPTICAL BISTABILITY

Ying-Hai Wang, HU CHENG-SHENG, Wang Zhicheng, 兰州大学物理系,兰州730001

Published Jan 1, 1992• 0 citations
Publisher

Abstract

We investigate the temporal aspects of absorptive two-photon optical bistability described by a semiclassical theory in the limit of a fully developed hysteresis cycle and when all decay rates have comparable magnitude. We show by multiple time-scale perturbation analysis that near the high-transmission branch the behavior of the system is governed by an equation for the field amplitude which determines the long-time evolution of the system, whereas, near the low-transmission branch all dynamical variables vary on the long time scale, and it is possible to describe the transition between the two stable branch by simple equations.

DOI
10.7498/aps.41.1598

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We investigate the temporal aspects of absorptive two-photon optical bistability described by a semiclassical theory in the limit of a fully developed hysteresis cycle and when all decay rates have comparable magnitude. We show by multiple time-scale perturbation analysis that near the high-transmission branch the behavior of the system is governed by an equation for the field amplitude which determines the long-time evolution of the system, whereas, near the low-transmission branch all dynamical variables vary on the long time scale, and it is possible to describe the transition between the two stable branch by simple equations.
We study the semiclassical mean-field theory of absorptive optical bistability in the limit of a fully developed hysteresis cycle, i.e., in the limit of large values of the bistability parameter CCC. We show by multiple time-scale perturbation analysis that it is possible to describe the transition between the two stable branches by simple equations. Near the low-transmission branch, the behavior of the system is governed by an equation for the atomic population, whereas, near the high-transmission branch, it is an equation for the field amplitude which determines the long-time evolution of the system. We then present an analytic study, completed by numerical results whenever necessary, of the time-dependent response of the system when the input field is swept across the bistable region. We study the influence of the initial conditions, the sweeping velocity, and the ratio of the atomic relaxation times on the dynamical hysteresis as well as its relation with the stationary hysteresis.
We study the semiclassical mean-field theory of single-mode dispersive optical bistability in the limit of a fully developed hysteresis cycle (i.e., in the limit of large values of the bistability parameter C) and when all decay rates have comparable magnitude. We locate (i) on the upper branch instabilities leading to time periodic regimes, (ii) on the lower branch instabilities leading to a switching before the limit point is reached. None of these instabilities are observed in the case of purely absorptive optical bistability.
Time\|dependent bifurcation and dynamical behaviors of the absorptive optical bistability equation are investigated systematically from the point of view of vector field.Internal relations for delayed bifurcation transitions are discussed.When the input optic field is constant,the existence of optical bistability and the phenomenon of critical slowing down are analyzed through a new way.When the input optic field is varied slowly with time linearly or periodically,different scaling relations are given by scaling balances.When the amplitude or frequency of the input optic field is varied slowly and linearly with time,the bifurcation and dynamical behaviors for the time\|dependent system of bistability are also studied .A new strange atractor is revealed..
We give a microscopic description of the optical bistability, where the transmission coefficient has two different values as a function of input light intensity, and the system exhibits a discontinuous jump with a hysteresis loop. We developed an efficient numerical algorithm to treat the quantum master equation for hybridized systems of many photons and a large number of two-level atoms. By using this method, we characterize the bistability from the viewpoint of eigenmodes and eigenvalues of the time-evolution operator of the quantum master equation. We classify types of optical bistability according to the photon number density in the cavity. In contrast to previous studies of optical bistability in the high-photon-density regime where the photons can be treated as a classical electromagnetic field and the resonance spectrum has a single-peak structure, we study the nature of optical bistability in the low-photon-density regime where the hybridization of photon and atom degrees of freedom occurs and the resonance spectrum has a double-peak structure. Unraveling the nature of the optical bistability in the latter regime may be important for the manipulation of quantum systems. Concretely, we discuss the steady-state properties of the optical bistability: dependencies of the photon number density on the intensity and the double-peak structure of the photon number distribution inside the bistable region. As for the dynamical properties, we find that the relaxation timescale shows an exponential growth with the system size and reveal how the hysteresis loop of the optical bistability depends on the size of the system and the sweeping rate of the driving amplitude. Finally, by investigating the effects of detuning frequency of the input field, we clarify the characteristic properties of the present optical bistability within the low-photon-density regime, which are qualitatively different from the standard optical bistable phenomena.
By means of the semiclassical method, we discuss the bistability in a two-photon laser with injected signal for the homogeneously broadened single mode ring cavity. It is demonstrated that in the resonant case one can find bistable states in a two-photon laser with injected signal. In the limit of "good cavity" and "bad cavity", we give a simple description of bistability leading to a predictions for the transient behavior of the output light and the hysteresis cycle by adiabatically eliminating the fast variables. It is found that the approach to the stationary state is monotonic in the low-branch and is oscillatory in the high-branch, and a critical slowing down occurs where the output field changes discontinuousiy.
Long-time behavior of transmitted and reflected field amplitude of optical bistability by a cavity including an absorptive resonant medium from an initial to a final steady state on switching the incident field is investigated by solving numerically the semiclassical dynamical equations without the mean-field approximation. The transmitted field amplitude as a function of time is monotonic as a whole, and an oscillatory character is seen on it in a shorter period. The dynamical character such as the oscillation amplitude and the duration of a whole process depend strongly on two parameters included in the equations.